What is the Greatest Common Factor of 76209 and 76224?

Greatest common factor (GCF) of 76209 and 76224 is 3.

GCF(76209,76224) = 3

We will now calculate the prime factors of 76209 and 76224, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76209 and 76224.

How to find the GCF of 76209 and 76224?

We will first find the prime factorization of 76209 and 76224. After we will calculate the factors of 76209 and 76224 and find the biggest common factor number .

Step-1: Prime Factorization of 76209

Prime factors of 76209 are 3, 7, 19, 191. Prime factorization of 76209 in exponential form is:

76209 = 3¹ × 7¹ × 19¹ × 191¹

Step-2: Prime Factorization of 76224

Prime factors of 76224 are 2, 3, 397. Prime factorization of 76224 in exponential form is:

76224 = 2⁶ × 3¹ × 397¹

Step-3: Factors of 76209

List of positive integer factors of 76209 that divides 76209 without a remainder.

1, 3, 7, 19, 21, 57, 133, 191, 399, 573, 1337, 3629, 4011, 10887, 25403

Step-4: Factors of 76224

List of positive integer factors of 76224 that divides 76209 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192, 397, 794, 1191, 1588, 2382, 3176, 4764, 6352, 9528, 12704, 19056, 25408, 38112

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76209 and 76224. The biggest common factor number is the GCF number.
So the greatest common factor 76209 and 76224 is 3.

Also check out the Least Common Multiple of 76209 and 76224